(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²）

(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2007²)(1-1/2008²）
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2007)(1-1/2007)(1+1/2008)(1-1/2008)
=(1+1/2)(1+1/3)……(1+1/2008)*(1-1/2)(1-1/3)(1-1/2008)
=3/2*4/3*5/4*……*2009/2008*1/2*2/3*3/4*……*2007/2008
=2009/2*1/2008
=2009/4016